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Since 2009, ESA has been conducting R&D activities leading towards the development of a European capability in radioisotope power systems for space. The programme is focused on the use of americium-241 as an innovative alternative to the plutonium-238 currently used by the USA and Russia. Two different technologies are being developed by the University of Leicester in the UK: radioisotope thermoelectric generators and radioisotope heater units. The development of the fuel containment architectures, known as heat sources, has recently evolved from the design stage to more representative prototypic systems. Multiple containment layers ensure that the heat sources can survive accident conditions from launch failures to Earth re-entry, minimising the risk of inadvertently releasing radioactive material into the environment. Validated accident models are necessary for the design iteration process of these systems, and for the creation of a safety case for their launch. The research project here presented was a collaboration, supported by ESA , between the University of Leicester in the UK and ArianeGroup in France. The goals of this activity were to perform the first-ever impact tests for the European Am-based heat sources, and to start developing computer models to simulate the behaviour of the containment systems under different impact conditions in accident scenarios. Tested samples were then characterized both at ESA/ESTEC and at the University of Leicester, in order to understand the behaviour of the fuel containment materials under the most relevant accident conditions.

In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature.

In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also presented to show that faster behaviour of the proposed method.

Every non-convex pair $(C, D)$ ( C , D ) may not have proximal normal structure even in a Hilbert space. In this article, we use cyclic relatively nonexpansive maps with respect to orbits to show the presence of best proximity points in $C\cup D$ C ∪ D , where $C\cup D$ C ∪ D is a cyclic T-regular set and $(C, D)$ ( C , D ) is a non-empty, non-convex proximal pair in a real Hilbert space. Moreover, we show the presence of best proximity points and fixed points for non-cyclic relatively nonexpansive maps with respect to orbits defined on $C\cup D$ C ∪ D , where C and D are T-regular sets in a uniformly convex Banach space satisfying $T(C)\subseteq C$ T ( C ) ⊆ C , $T(D)\subseteq D$ T ( D ) ⊆ D wherein the convergence of Kranoselskii’s iteration process is also discussed.

In the past decade, numerous studies have shown that incorporating geogrid in the pavement could effectively improve the pavement performance. The major benefit of using geogrid in the flexible pavement is to improve its rutting performance as the result of the reinforcement function of geogrid. Mechanical-empirical pavement design guide (MEPDG) developed to provide the pavement performance prediction throughout its design life. However, MEPDG is not able to consider the effect of incorporating geogrid in the flexible pavement. In this study, a design procedure was proposed to obtain an equivalent geogrid pavement structure, which satisfies MEPDG design input requirements. In this procedure, a 2D finite element method was used to simulate geogrid reinforced and non-reinforced pavement structures. The iteration process based on stress–strain analysis of finite element model (FEM) used to obtain an equivalent structure input for MEPDG. The geogrid reinforced rutting performance can be predicted by analyzing the equivalent geogrid structure using MEPDG. A significant life improvement of pavement with geogrid was observed compared to pavement without geogrid. The results showed that the incorporating of geogrid in asphalt pavement layer significantly reduce the rutting of pavement layer, thus will contribute to extension of pavement service life.

Retinal vessel segmentation is part of the morphological extraction of retinal blood vessels that plays an essential role in medical image processing. Manual segmentation is possible to do, but it is time-consuming and requires special operators. Moreover, the possibility of variability between operators is vast. This study aims to answer the shortcomings of the manual segmentation process by automatically segmenting retinal blood vessels. The main contribution of this study is the use of a simple method to iteratively segment retinal blood vessels. All processes in the segmentation are simulated using Matlab. The algorithm was evaluated by comparing the results of the automatic segmentation with 20 manually segmented images from the STARE dataset. The result show specificity 98.13%, accuracy 93.60%, sensitivity 56.42%, precision 80.48%, and the dice coefficient 64.06%. In conclusion, the automatic retinal blood vessel image segmentation process worked well.

Let S be a nonempty subset of a CAT(0) space E. A mapping T : S → S is said to satisfy condition(C) (sometimes called Suzuki-generalized nonexpansive) ifIn this work, we obtain fixed point and conv...

A resilience and seismic safety evaluation method of under-qualified concrete structures designed based on codes prior to the introduction of earthquake provisions is presented. A numerical method for evaluating and improving a structure’s performance and resilience through jacketing and Carbon Fiber Reinforced Polymers (CFRP) retrofitting was developed. The model analyzed the structure’s existing condition, inadequate elements were identified, and segments that required strengthening were determined. Retrofitting and external reinforcing techniques were applied, and their effectiveness evaluated. Elements identified as insufficient were subjected to a strengthening iteration process to ensure that all qualifications were fulfilled. It was proven that the numerical simulation was accurate, cost-effective and time-saving in evaluating deficient structures and the effectiveness of their strengthening methods. The numerical model and analysis in conjunction with the technology of jacketing and CFRP retrofitting provide a fast and straightforward solution for older structures in ameliorating their resilience and overall performance

*Maldar, Samet ( Aksaray, Yazar ), The aim of this paper is twofold: (a) to revisit the results in Iqbal et al. (Numer Algorithms 1–21, 2019. https:doi.org/10.1007/s11075-019-00854-z) and prove some convergence and stability results for the subclass of multivalued contractive operators under some mild conditions (b) to introduce a multivalued Reich-Suzuki type α-nonexpansive mappings and present some fixed point results for this class of mappings. We considered a more natural notion of stability called weak w2-stability instead of simple stability in Iqbal et al. (Numer Algorithms 1–21, 2019. https:doi.org/10.1007/s11075-019-00854-z). Some illustrative examples to support the results obtained herein are also presented.

This paper describes statistical attempts of estimating the critical frequency of the F2 layer ( foF 2 ) using Global Positioning System (GPS) Total Electron Content (TEC), with the help of electron density model NeQuick2, for monthly hourly median conditions. The stations under study are Islamabad (geog. lat: 33.66° N, long: 73.23° E, geomag. lat: 25.21° N) and Darwin (geog. lat: 12.46° S, long: 130.85° E, geomag. lat: 21.96° S) for the years 2011 to 2014. As first approximation, a linear regression analysis between ionosonde foF 2 values and GPS TEC produced a regression coefficient that lies between 77% to 83% at Darwin and between 81% and 87% at Islamabad. Two methods were used for the same purpose - First, using GPS TEC and NeQuick2 slab thickness, which produced the Root Mean Square Error (RMSE) of less than 1 MHz at Islamabad, but greater than 1 MHz for Darwin. Second, using an iteration process by ingesting GPS TEC in NeQuick2 to improve foF 2 such that optimum foF 2 obtained by iteration process has corresponding NeQuick2 TEC, which is close to GPS one within ±5%. This provides foF 2 estimation with 84% confidence over Islamabad. The results show that the attempts are inspiring for obtaining reliable foF 2 from GPS TEC over Islamabad.

Utility encounters situations like when one out of two power transformers in the substation requires maintenance and only one transformer remains in operation. To meet the load requirements of a maximum number of customers, if not all, the only transformer needs to be overloaded. Due to various load types within the service territory, utilities need to understand the customers' maximum dynamic loading amount to overload a transformer in an emergency. We propose the iteration process with real-world substation data, which considers the concept of a coordinated substation for optimal power flow. We found to what extent the only 138 kV//13.8 kV, 30/40/50 MVA transformer can be safely overloaded beyond its nameplate's maximum rating for a minimum time. Within that time, the utility personnel can work on the substation yard and switchgear room safely and comfortably to bring back the other transformer in operation. We found from the perspective of power flow that with increased dynamic loading, transformer secondary current increases. Therefore, under the maximum dynamic loading condition, we should calculate the asymmetric fault current on the 13.2 kV switchgear bus to select the suitable CTs and develop a protection scheme accordingly.

In this paper we introduce a new iterative algorithm for approximating fixed points of ?-?-contractive type mappings in CAT(0) spaces. We prove a ?-convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.

The motive of this paper is to study the convergence analysis of a modified iteration procedure for total asymptotically nonexpansive mapping under some suitable conditions in the setting of CAT(0) spaces. By using MATLAB R2018a, we also illustrate numerical experiment to compare the rate of convergence of the new iteration process with some existing iteration processes.

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalized Suzuki nonexpansive mappings on hyperbolic spaces. Strong and Δ-convergence theorems are proved using the Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with CAT(0) spaces.

In this article, Δ-convergence and strong convergence of the modified Ishikawa iteration process with errors are established for continuous mappings of asymptotically nonexpansive type in CAT(0) spaces. Our results extend and improve the previous results given by many authors.

In this paper, the application of the S-iteration process for solving the Power Flow (PF) problemis comprehensively studied. Thus, a combined approach between the S-iteration processand Newton's method (SIP-NR) is adapted for solving PF equations. Moreover, drawbacksshown by SIP-NRunder heavy loading conditions due to its linear convergence are addressed by developing a simple but reliable technique called Modified SIP-NR(MSIP-NR). MSIP-NR uses anon-repeatedly updating Jacobianscheme with the aim toaccelerate the convergence of SIP-NR. The introduced PF techniques are validated using well and ill-conditioned systemsunder several demand scenarios. The obtained results prove the robustness and efficiency of the introducedPF techniquescompared with other well-known methodologies. On the light of the results obtained, the introduced PF techniques may be used for different applications in power system analysis. Some of these potential applications are enumerated and discussed.

In this paper, we establish $$\bigtriangleup $$ -convergence and strong convergence of Kirk type iteration process in CAT(0) spaces. We apply our results to solve consistent and inconsistent convex feasibility problems in CAT(0) spaces. This work improves and extends the corresponding results of Kirk, Kuhfittig, Rhoades and Takahashi and Tamura on a nonlinear domain.

In this paper, we propose a new iteration process which is faster than the leading S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79], Thakur et al. [App. Math. Comp. 275 (2016), 147-155] and M [Filomat 32, no. 1 (2018), 187-196] iterations for numerical reckoning fixed points. Using new iteration process, some fixed point convergence results for generalized α-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes.

In the field of brain-computer interfaces, it is very common to use EEG signals for disease diagnosis. In this study, a style regularized least squares support vector machine based on multikernel learning is proposed and applied to the recognition of epilepsy abnormal signals. The algorithm uses the style conversion matrix to represent the style information contained in the sample, regularizes it in the objective function, optimizes the objective function through the commonly used alternative optimization method, and simultaneously updates the style conversion matrix and classifier during the iteration process parameter. In order to use the learned style information in the prediction process, two new rules are added to the traditional prediction method, and the style conversion matrix is used to standardize the sample style before classification.

The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by a given graph: A family of symmetric hypermatrices is associated with a uniform hypergraph and zeros are forced in a null vector. The value of the hypergraph zero forcing number and maximum nullity are determined for various families of uniform hypergraphs and the effects of several graph operations on the hypergraph zero forcing number are determined. The hypergraph zero forcing number is compared to the infection number of a hypergraph and the iteration process in hypergraph power domination.

Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper, we present a novel weighted $l_1$-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods.

The rapid growth of distributed energy resources results in the proliferation of prosumers at the distribution level, who can both produce and consume energy. In order to harvest benefits of aggregation to obtain revenues in wholesale market and encourage direct interactions among prosumers and other flexible players at the same time, this paper proposes an aggregation framework for prosumers based on transactive energy, in which prosumers aggregate and trade in an independent, proactive and privacy-preserved manner without relying on a real central entity, while other flexible players could be benefited equally. The aggregation of prosumers as a whole behaves as a retailer that trades in wholesale market and towards end-users in retail market. Therefore, the problem is generalized as a bi-level multi-leader multi-follower game in which prosumers are leaders and end-users are followers. To realize the transactive energy based trading framework, an inner-outer iteration approach is proposed, where the outer iteration involves interactions among prosumers and end-users, and achieves final results including the retail price and optimal behaviors of all players. The inner iteration is conducted during each time of the outer iteration to solve end-users’ optimal consuming profiles. The whole iteration process involves the independent decision makings of players, and only relies on exchange of information of retail price and prosumers’ offers instead of players’ private information. Case studies are then carried out demonstrating the proposed transactive energy based aggregation framework for prosumers could decrease the retail price, increase revenues for both prosumers and end-users, and reduce the peak load.

In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.

We propose a numerical continuation method for a nonlinear system that consists of scalar and functional equations. At each parameter step, we solve the system by a modified Gauss–Seidel method. An advantage of this method is that the system is divided into two parts and each part is solved by a suitable numerical method with a desired precision. We solve the functional equations self-consistently at each step of the iteration process for the system of scalar equations. We apply the proposed method for calculating temperature dependence of magnetic characteristics of metals in the dynamic spin-fluctuation theory.

In this paper, we extend the study of an iteration process introduced by Thakur-Thakur-Postolache [J. Inequal. Appl., (2014), 147–155] from the class of nonexpansive operators to the more general c...

The purpose of this paper is to introduce the modified Agarwal-O’Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of Panyanak (J. Fixed Point Theory Appl. (2018)). At the end of the paper, we offer an example to illustrate the main results.

The purpose of this paper is to modify Abbas iteration for two G-nonexpansive mappings. We perform the convergence analysis of newly defined iteration process in uniformly convex Banach space. To compare the rate of convergence of the proposed method with well known Ishikawa iteration, modified S-iteration and Thianwan new iteration processes, a numerical example is also constructed.

In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of Suzuki generalized nonexpansive mappings. Again we reconfirm our results by example and table. Further, we utilize our proposed algorithm to solve delay differential equation.

In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms for contractive-like mappings. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of generalized $\alpha$-nonexpansive mappings. Again we reconfirm our results by an example and table. Further, we utilize our proposed algorithm to solve split feasibility problem.

This paper is concerned with the existence/nonexistence of positive solutions of a weighted Hardy-Littlewood-Sobolev type integral system. Such a system is related to the extremal functions of the weighted Hardy-Littlewood-Sobolev inequality. The Serrin-type condition is critical for existence of positive solutions in \begin{document}$ L_{loc}^\infty(R^n \setminus \{0\}) $\end{document} . When the Serrin-type condition does not hold, we prove the nonexistence by an iteration process. In addition, we find three pairs of radial solutions when the Serrin-type condition holds. One is singular, and the other two are integrable in \begin{document}$ R^n $\end{document} and decaying fast and slowly respectively.

An explicit discontinuous deformation analysis (DDA) that uses an explicit time integration procedure and an explicit calculation of interaction forces between blocks is proposed to overcome the limitations of conventional implicit DDA in simulating large-scale problems. The advantages of the explicit DDA are that (1) the global equilibrium equations are unnecessary to be assembled and the solving for unknowns of every block can be performed independently and conveniently, thereby reducing the computational effort and memory requirement; (2) the open-close iteration process is avoided because the interaction forces between blocks are calculated explicitly according to the initial information at the start of the current time step. The efficient parallel computing is very appropriate for the explicit DDA. To further improve its computational efficiency, the explicit DDA is paralleled based on OpenMP. The accuracy of the explicit DDA is verified through several numerical examples with analytical solutions, experimental data or field observation. Further, the computational efficiency is demonstrated by a series of models and the parallel speedup factor on 6 OpenMP threads is approximately 4.2. Conclusively, the explicit DDA is promising for analyzing blocky systems in large scale.

In this paper, we propose a three-step iteration process and show that this process converges faster than a number of existing iteration processes. We give a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating common fixed points for two nonexpansive mappings. Again we reconfirm our results by examples and tables. Further, we provide some applications of the our iteration process.

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our results‎. ‎Our results improves many known results of the existing literature‎.

In recent studies, the competitiveness of the Newton-S-Iteration-Process (Newton-SIP) techniques to efficiently solve the Power Flow (PF) problems in both well and ill-conditioned systems has been highlighted, concluding that these methods may be suitable for industrial applications. This paper aims to tackle some of the open topics brought for this kind of techniques. Different PF techniques are proposed based on the most recently developed Newton-SIP methods. In addition, convergence analysis and a comparative study of four different Newton-SIP methods PF techniques are presented. To check the features of considered PF techniques, several numerical experiments are carried out. Results show that the considered Newton-SIP techniques can achieve up to an eighth order of convergence and typically are more efficient and robust than the Newton–Raphson (NR) technique. Finally, it is shown that the overall performance of the considered PF techniques is strongly influenced by the values of parameters involved in the iterative procedure.

In this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki’s condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated.

To predict how many consumers will buy goods in the next month helps the e-commerce platform discover potential buyers and carry out the corresponding strategic activities. After analyzing and cleaning the data, we select user purchase features to use eXtreme Gradient Boosting (XGBoost) algorithm to train the divided data sets. Meanwhile, we choose Light Gradient Boosting Machine (LightGBM), Long Short-Term Memory (LSTM) and Fully Connected Neural Network (FCNN) as comparison algorithms. Expectedly, the experiments indicate that using the XGBoost algorithm to predict purchasing can improve performance. Specifically, LightGBM and LSTM increase significantly before remaining stable, whereas FCNN begins in the highest number falling dramatically to approximately the accuracy of 0.32 and keeps steady. Throughout the iteration process, the accuracy of XGBoost surpassed FCNN, and experienced a moderate increase from 0.55 to 0.67, increasing the accuracy by 12%.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of $\operatorname{CAT}(0)$ CAT ( 0 ) spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.

The goal of this article is to consider an Ishikawa type iteration process with errors to approximate the fixed point of -asymptotically quasi non-expansive mapping in convex cone metric spaces. Our results extend and generalize many known results from complete generalized convex metric spaces to cone metric spaces.

In recent years many researchers have focused their attention on the use of different iteration process – known from fixed point theory – in the generation of different kinds of patterns. In this paper, we propose modifications of the Bisheh-Niasar and Saadatmandi root finding method. In the first modification we modify the formula of the method and in the second modification we use the S -iteration with periodic parameters. Moreover, we numerically investigate some properties of the proposed methods and modification using three measures, i.e., the generation time, mean number of iterations and convergence area index. The obtained polynomiographs show that the proposed methods have a potential artistic applications, and the numerical results show that there is no obvious dependency of the considered measures on the sequences of the parameters used in the S -iteration.

This Paper studied the mutual influence between uncertain environment, enterprise dynamic innovation capabilities and innovation strategies and established a theoretical framework based on uncertain environment, enterprise dynamic innovation capabilities and innovation strategies. This framework will be used to analyze the support of an enterprise's dynamic innovation capabilities for its innovation strategies behaviors under the transition period of uncertain environment. Based on the theoretical framework, an in-depth study was conducted on the case of Qihoo 360's micro-innovation based on “free and secure” products. According to analysis of specific Qihoo 360 “micro-innovation”, we understood that dynamic innovation capabilities are the support maintaining an enterprise's competitiveness. Furthermore, it was found that Qihoo 360 became the leading figure in the internet security industry by providing an “iteration process” of all products on a “non-payment” and “security” basis. This Paper contributed to the further enrichment of the connotations of dynamic innovation capabilities and analysis of the mechanism of micro-innovation strategy, and the dynamic supporting mechanism of enterprise dynamic innovation capabilities on its micro-innovation strategy is studied under the background of uncertainty environment. It provides theoretical support and practical guidance for Internet enterprises to carry out innovation activities in an uncertain environment.

Current research focuses on expert estimation of indicators by employing a limited number of qualified experts, which involves considerable time and cost. The advent of modern information technology allows rapid and efficient assessment of indicators that characterize performance of enterprises. The main tool for solving the issue related to the credibility of such an estimation is the development of new methods for processing its results. We have proposed a method of distances to treat the results from expert estimations of indicators and examined the results of its work. To this end, theoretical substantiation of the method has been performed, based on the concept of proximity (distances) among estimates relative to the average value, coefficients of experts' competence, and normalization of the point scale of assessment. We have explored three variants of expert point- and verbal-based estimates of independent and dependent indicators in line with the method of distances, which showed that the convergence rate of iteration process for all cases varies from 1 to 4 orders of magnitude at each iteration. That makes it possible to draw a conclusion about a very small number of computations by the information system and sufficient speed of processing expert estimates. A comparative analysis of the method of distances with a similar method of square deviations has revealed almost the same rate of convergence up to 3‒5 iterative steps, but the proposed method yields an estimate close to the average estimate of each indicator. It also enables the processing of results in information systems by 99 % faster, from dozens, even hundreds of times, more estimates than that in the methods of expert selection, which is important under current competitive environment. Average efficiency of the method compared to the method of expert selection is 5.8 %

This paper aims to propose new numerical procedures for elasto-plastic analysis of the interactions between fully-grouted bolt and rock with slip and non-slip cases at a potential-failure interface. In the proposed procedure with the slip case, the iteration process accounts for the elongation of the bolt, and the calculation process is greatly simplified by considering only the initial and final states (i.e., no intermediate finite states as is the case for existing procedures) without compromising the accuracy of the predictions. In the proposed procedure with the non-slip case, the elasto-plastic solution of the plastic rock strain is rigorously derived; the two scenarios in which the length of the rock bolt is contained within the plastic zone or within the elastic zone are comprehensively considered. The obtained solutions of tensile force in the bolt, shear stress at the potential-failure interface, rock displacement and stress components in the rock from the proposed procedures are validated by analyses with purely analytical methods and a commercial finite-difference program. With influences of rock quality and plastic softening behaviour of rock mass, the differences of the solutions in the slip and non-slip cases at potential-failure surface are compared; the dependency of the relative movement on the shearing stiffness at the potential failure interface is also investigated.

Delphi technique was developed in 1950 by researchers at the Rand Corporation led by Norman Delkey and Olaf Helmer and has since been used in hundreds of businesses forecasting in the public and private sectors. Delphi technique is a judgmental forecasting procedure for obtaining, exchanging, and developing an informed opinion about future events. Therefore, the Delphi technique is a systematic way to get a consensus of opinion among the experts who have related interests through a panel discussion. The objective of most Delphi is the reliable and creative exploration of ideas or the production of suitable information for decision making. The key features of the Delphi technique, namely: (1) systematic, (2) questionnaire, (3) expert judgment, (4) iteration process, and (5) feedback. Baseline characteristics of the Delphi technique (conventional) there are five, namely: (1) anonymity, (2) iteration, (3) controlled feedback, (4) statistical group response, and (5) expert consensus. While the characteristics of a policy Delphi also five, namely: (1) selective anonymity, (2) informed multiple advocacies, (3) polarized statistical response, (4) structured conflict, and (5) computer conferencing. Steps in the application of policy Delphi there are seven, namely: (1) issue specification, (2) selection advocates, (3) questionnaire design, (4) analysis of first-round results, (5) development of subsequent questionnaires, (6) organization of group meetings, and (7) preparation of final report.

Reliability-based design optimization (RBDO) is a powerful tool to handle the influence of various uncertainties during optimization. However, unbearable computation cost is one of the largest barriers for its application, especially for the finite element method (FEM)-based RBDO. In this paper, an efficient and accurate RBDO framework is established based on isogeometric analysis (IGA) for complex engineering problems. Furthermore, an enhanced step length adjustment (ESLA) iterative algorithm and a second-order reliability method-based stepped-up sequential optimization and reliability assessment approach (SSORA-SORM) are proposed to boost the efficiency of RBDO. According to the situation of iteration process, the step length of search the most probable target point can be adaptively updated by the proposed criterion to improve the robustness in ESLA. In the proposed framework, the analytical first-order sensitivity is derived based on IGA in the optimization process to substitute the time-consuming finite difference method. The robustness, accuracy and efficiency of proposed methods are verified via several numerical benchmarks. Besides, three complex IGA-based examples demonstrate that the proposed method is able to save much computational cost without losing accuracy, which is inherently suitable for the RBDO of complex engineering problems.